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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Simultaneous extensions from discrete subspaces


Author: H. Banilower
Journal: Proc. Amer. Math. Soc. 36 (1972), 451-455
MSC: Primary 53C20; Secondary 46E15
MathSciNet review: 0319138
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Abstract: If N is a denumerable, discrete, normally embedded subspace of the completely regular space S, then any bounded linear operator from $ C(N)$ into $ C(S)$ that extends functions in $ {C_0}(N)$ necessarily extends all bounded functions on some infinite subset of N (that are zero elsewhere on N). For compact S, such operators exist whenever $ C(S)$ contains a subspace isometric to (m). It is also shown, assuming the continuum hypothesis, that if S is a locally compact F-space and $ {C_0}(S)$ is complemented in $ C(S)$, then S is countably compact.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0319138-5
PII: S 0002-9939(1972)0319138-5
Keywords: Simultaneous extension, discrete subspace, F-space, subspace isometric to (m)
Article copyright: © Copyright 1972 American Mathematical Society